There are alot of paradoxes that come with time travel. Its not the idea of time travel its more of the idea of multi-dimesional travel.
What we think of time travel is actually really multi-dimensional travel. Because the only time that exists is now. Theres only one moment in the universe.
Heres a famous paradox on time travel, its called the Grand Father Paradox.
So time travel does exist and it is possible but its actually multi-dimesional travel. You travel to another dimension or parralell reality is whats the idea.